Abstract
Flat bands (FB) are strictly dispersionless bands in the Bloch spectrum of a periodic lattice Hamiltonian, recently observed in a variety of photonic and dissipative condensate networks. FB Hamiltonians are fine-tuned networks, still lacking a comprehensive generating principle. We introduce a FB generator based on local network properties. We classify FB networks through the properties of compact localized states (CLS) which are exact FB eigenstates and occupy unit cells. We obtain the complete two-parameter FB family of two-band networks with nearest unit cell interaction and . We discover a novel high symmetry sawtooth chain with identical hoppings in a transverse dc field, easily accessible in experiments. Our results pave the way towards a complete description of FBs in networks with more bands and in higher dimensions.
- Received 5 October 2016
- Revised 16 February 2017
DOI:https://doi.org/10.1103/PhysRevB.95.115135
©2017 American Physical Society